SOLUTION: Please help prove identity: {{{2sin(2x)cos(2x)=4cos(x)(sin(x)-2(sin(x))^3)}}} thank you

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Question 232805: Please help prove identity:
2sin%282x%29cos%282x%29=4cos%28x%29%28sin%28x%29-2%28sin%28x%29%29%5E3%29
thank you
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
2sin%282x%29cos%282x%29=4cos%28x%29%28sin%28x%29-2%28sin%28x%29%29%5E3%29
Two formulas you need are sin%282x%29=sin%28x%29cos%28x%29 and the other is cos%282x%29=1-2%28sin%28x%29%29%5E2%29
Using these we can rewrite the left side to become.
2%2A2sin%28x%29cos%28x%29%281-2%28sin%28x%29%29%5E2%29 2%2A2=4
4sin%28x%29cos%28x%29%281-2%28sin%28x%29%29%5E2%29 Now we distribute the sin%28x%29 that is on the outside.
4cos%28x%29%28sin%28x%29-2%28sin%28x%29%29%5E3%29 this proves your identity.